Searching for linearly separable subsets using the class of linear separability method

In a non linearly separable two-class classification problem, a subset of one or more points, belonging to one of the two classes, which is linearly separable from the rest of the points (the two classes combined), can always be found. This is the basis for constructing recursive deterministic perceptron neural networks. In this case, the subsets of maximum cardinality are of special interest as they minimise the size of the topology. An exhaustive strategy is normally used for finding these subsets. This paper shows how the class of linear separability method, for testing linear separability, can be used for finding these subsets more directly and efficiently.